To determine how many times Erin should expect to roll the number cube to get a prime number 12 times, we first need to identify how many prime numbers are on a six-sided die.
The prime numbers on a six-sided die (which has the numbers 1 through 6) are:
- 2
- 3
- 5
There are three prime numbers (2, 3, and 5) out of a total of six faces. This means the probability \( p \) of rolling a prime number is:
\[ p = \frac{3}{6} = \frac{1}{2} \]
Now, we want Erin to roll a prime number 12 times. The expected number of rolls \( E \) needed to roll a prime number \( k \) times is given by the formula:
\[ E = \frac{k}{p} \]
Here, \( k = 12 \) (the number of desired prime rolls) and \( p = \frac{1}{2} \).
Plugging in the values:
\[ E = \frac{12}{\frac{1}{2}} = 12 \times 2 = 24 \]
Thus, Erin should expect to roll the number cube approximately
\[ \boxed{24} \]
times to result in a prime number 12 times.